Question

On a certain nonstop trip, Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours. What was her average speed, in miles per hour, for the entire trip?
(1) $2x+3y=280$
(2) $y=x+10$

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

Answer: (A)

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

• Marta traveled a total of $(2x+3y)$ miles in $2+3=5$ hours for an average speed of miles per hour. Thus, we have to determine the value of .

1. Given that $2x+3y=280$, it follows that . Thus, statement 1 is sufficient.
2. Given that $y=x+10$, it follows that . Therefore, the value of could be a variable depending on the value of x and y. Thus, statement 2 is insufficient.

• The correct answer is A; statement 1 alone is sufficient.